Remark For probability measures on \(\mathbb {R}\) , \(p_1\)  and \(p_2\)  must obey the following requirements in Theorem 3.1 of [1]}:
\(\bigg (\pi _0(x) \int _{-\pi }^x (h(y)-\mathbb {E}[h(X_1)])p_1(y) dy\bigg )^{\prime } \in L^1(P_2)\) 
